Suppose that a Bayesian spam filter is trained on a set of 5000 spam messages and 7500 messages that are not spam. The word "achievement" appears in 1000 spam messages and 150 messages that are not spam, while the word "research" appears in 800 spam messages and 300 messages that are not spam. Estimate the probability that a received message containing both the words "achievement" and "research" is spam. Will the message be rejected as spam if the threshold for rejecting spam is 0.9?

A First Course in Probability (10th Edition)
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ISBN:9780134753119
Author:Sheldon Ross
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Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Suppose that a Bayesian spam filter is trained on a set of 5000 spam messages and 7500
messages that are not spam. The word "achievement" appears in 1000 spam messages and 150
messages that are not spam, while the word “research" appears in 800 spam messages and 300
messages that are not spam. Estimate the probability that a received message containing both
the words "achievement" and "research" is spam. Will the message be rejected as spam if the
threshold for rejecting spam is 0.9?
Transcribed Image Text:Suppose that a Bayesian spam filter is trained on a set of 5000 spam messages and 7500 messages that are not spam. The word "achievement" appears in 1000 spam messages and 150 messages that are not spam, while the word “research" appears in 800 spam messages and 300 messages that are not spam. Estimate the probability that a received message containing both the words "achievement" and "research" is spam. Will the message be rejected as spam if the threshold for rejecting spam is 0.9?
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